Evolution by natural selection (adaptive evolution) is one of the major generalizations in biology. It also has important ramifications for medicine, agriculture, and biotechnology. Unfortunately, many outcomes of natural selection have been to our detriment. The most obvious ones are apparent in medicine - the evolution of drug-resistant bacteria and viruses, to the point that some infections are now untreatable. Yet, whatever problems arise from natural selection of pests and parasites, we need not remain as helpless victims to its effects: understanding evolution offers potential solutions. Our ability to predict adaptive evolution is still in its infancy. Yet it is now apparent that many opportunities exist for improving that understanding, aided by molecular biology. This proposal integrates theoretical and experimental methods to explore properties of adaptive evolution. Although population genetic theory has long given us a foundation for describing adaptive and non-adaptive evolution, that theory is concerned with predicting the course of gene frequency evolution after the beneficial effects and other properties of those genes are specified. Here we ask whether there are general, statistical properties about the numbers and effects of beneficial mutations. While it might seem that the characteristics of beneficial mutations will vary idiosyncratically from system to system, recent work by Orr using statistical theory suggests that there may indeed be generalities that transcend the biological details of a system. Exploring the nature of these generalities leads to the following objectives: Aim 1: Characterize the properties of the first step in an adaptive walk. Aim 2: Investigate the relationship between first step beneficial mutations and subsequent steps in an adaptive walk. Each aspect of the proposed research integrates mathematical models and statistical methods with experimental evolution of bacteriophages and total genome sequencing. If the above mentioned generalities hold, they will have broad implications for our general understanding of molecular evolution. This theory may also suggest useful approaches to predict the trajectory of evolution in organisms of medical importance. Such information could be extremely useful at early stages of drug development, as well as in designing treatments that are more resilient to evolution in the target species.